Yukawa potential

In particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential named after the Japanese physicist Hideki Yukawa. The potential is of the form:

${\displaystyle V_{\text{Yukawa}}(r)=-g^{2}{\frac {e^{-\alpha mr}}{r}},}$

where ${\displaystyle g}$ is a magnitude scaling constant, i.e. is the amplitude of potential, m is the mass of the particle, r is the radial distance to the particle, and α is another scaling constant, so that ${\displaystyle r\approx {\tfrac {1}{\alpha m}}}$ is the approximate range. The potential is monotonically increasing in r and it is negative, implying the force is attractive. In the SI system, the unit of the Yukawa potential is (1/meters).

The Coulomb potential of electromagnetism is an example of a Yukawa potential with the ${\displaystyle e^{-\alpha mr}}$ factor equal to 1, everywhere. This can be interpreted as saying that the photon mass m is equal to 0. The photon is the force-carrier between interacting, charged particles.

In interactions between a meson field and a fermion field, the constant ${\displaystyle g}$ is equal to the gauge coupling constant between those fields. In the case of the nuclear force, the fermions would be a proton and another proton or a neutron.